Celestia Forums

Is it possible that an analytical solution for the N-body problem does exist, but has thus far eluded our brightest mathamaticians? Or has it been proven that an analytic solution can not exist?

Yes, there's a proof from Henri Poincar?, showing there is no analytical solution for the 3-bodies problem (so no analytical solution for the N-bodies problem too).

We can only have an analytical solution for some very special cases.

This is part of an important theory in classical mechanics, called "Dynamical chaotic systems", or "Chaos theory".